[3.5]when a construct become an outsider by certain spells....

[Viscerator]

Greeting guys! Suppose I am a construct with no constitution for sure. Now I cast visage of the deity, greater in SPC on myself. It gives me the outsider type. Now I will come to be an outsider without constitution?

[BowStreetRunner]

Your creature type changes for the duration of the spell. So all traits you have of the Construct type would go away and instead you would have the traits of the Outsider type. So your normal constitution (prior to applying the Construct traits) would be restored. As a PC you should have still rolled a Con score (or purchased with point-buy) before applying the Construct traits, so you would go back to this. If you never had one because you never thought you would need it, get with your DM to establish what it should be any time an effect like this applies.